Macbook Pro 15" (mid-2010) won't charge after battery died?

I have had this problem several times since earlier this year. I let my Macbook Pro die completely, and when I go to plug it in later to charge it simply doesn't charge.

The LED on the adapter shows a faint, slightly flashing green light. The battery indicator lights on the side of the Macbook do not light up at all, and the computer does not start even after letting it "charge" for a while.

It is no longer under warranty with Apple so I have had to bring it to the store at which I purchased it (Future Shop). Since the first time I've had this issue, I have recieved three new MagSafe adapters, all of which worked fine in the beginning but resulted in the same issue after a few months. The techs at Future Shop have informed me that they have checked the macbook each time I have sent it in and see no issues with it.

I'm at a loss, seeing as it has happened again. I'm beginning to think I'm dealing with a faulty battery, but I'm not understanding why each new adapter seems to resolve the issue temporarily.

Constantly having to send my macbook in to be "fixed" is getting frustrating, seeing as I'm left without it for 2 weeks only to get it back and be faced with the same issue over and over again.